In this latter case it is difficult to identify a threshold because rainfall events that result in landslides are not clearly distinguished from those that do not. Finally, we resort to a numerical example to support our theoretical results. Rainfall intensity-duration thresholds in the two conceptual cases of debris flows triggered by (a) channel runoff and (b) deep-seated landslides. Besides, we show that the proposed model undergoes a forward supercritical transcritical bifurcation when the bait casting rate is equal to the critical value. Then we define the net reproductive rate R 0 determining the survival of the model and reveal the relationship between R 0 and the bait casting rate. We first prove the well-posedness of the proposed model. To this end, in this letter, we formulate a diffusive bait-fish model with advection term, aiming to determine the bait casting threshold that meets the demand for the breeding and causes less pollution to the water environment. However, the main issue for the fishermen to be concerned about is the determination of the reasonable amount of casting bait since excess feeding bait will not only deteriorate water quality but also increase farming costs while too little bait casting cannot meet the demand for capture. Cage culture, as a kind of aquaculture, is increasingly becoming the main way to provide aquatic products due to its merits of high output and easy management.
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